It sounds like the veneer is bubbling.

Did any moisture get on the table or under the tablecloth?

Define bumps.

Exposure to soft plastics can damage the finish is what is known as "packing marks." They can usually be removed by rubbing and/or applying more finish.

But this is only a guess at the cause, there are many possible explanations.

Moisture, quite possibly.

These bumps sometimes trail and are sticking out of the wood, by trailing I mean let's say you put a dish on the table the circle pressure points show on the table, as well as random bumps all over the table.

If put my nail on a bump to bring it down, it feels waxy and sort of smudges on the table.

I have done some more research and have a sneaking suspicion that it might be plasticizer migration but I'm not sure. The finish also is lacquer.

Suggestions?

Could it be they were their when you first received the table? Does the finish feels bumpy or rough ? One common problem; the finished was applied in an unclean environment, so what your feeling is the small bits of particles under the finish.